Trigonometric Identities Flashcards
Reciprocal Identity
sinu =
= 1/cscu
Reciprocal Identity
cosu =
= 1/secu
Reciprocal Identity
tanu =
= 1/cotu
Reciprocal Identity
cscu =
= 1/sinu
Reciprocal Identity
secu =
= 1/cosu
Reciprocal Identity
cotu =
= 1/tanu
Quotient Identity
tanu =
= sinu/cosu
Quotient Identity
cotu =
= cosu/sinu
Pythagorean Identity
sin^2u + cos^2u =
= 1
Pythagorean Identity
tan^2u + 1 =
= sec^2u
Pythagorean Identity
1+ cot^2u =
= csc^2u
Cofunction Identity
sin(π/2 - u) =
= cosu
Cofunction Identity
cos(π/2 - u) =
= sinu
Cofunction Identity
tan(π/2 - u) =
= cotu
Cofunction Identity
cot(π/2 - u) =
= tanu
Cofunction Identity
csc(π/2 - u) =
= secu
Cofunction Identity
sec(π/2 - u) =
= cscu
Even/Odd Identity
sin(-u) =
= -sinu
Even/Odd Identity
csc(-u) =
= -cscu
Even/Odd Identity
cos(-u) =
= cosu
Even/Odd Identity
sec(-u) =
= secu
Even/Odd Identity
tan(-u) =
= -tanu
Even/Odd Identity
cot(-u) =
= -cotu
Sum & Difference Formula
sin(u +- v) =
= sinucosv +- cosusinv
Sum & Difference Formula
cos(u +- v) =
= cosucosv -+ sinusinv
Sum & Difference Formula
tan(u +- v) =
= (tanu +- tanv)/(1 -+ tanutanv)
Double-Angle Formula
sin2u =
= 2sinucosu
Double-Angle Formula
cos2u =
= cos^2u - sin^2u
= 2cos^2u - 1
= 1 - 2sin^2u
Double-Angle Formula
tan2u =
= (2tanu)/(1 - tan^2u)
Half-Angle Formula
sin(u/2) =
= +- √(1 - cosu)/2
Half-Angle Formula
cos(u/2) =
= +- √(1 + cosu)/2
Half-Angle Formula
tan(u/2) =
= (1 - cosu)/sinu
= sinu/(1 + cosu)
Power-Reducing Formula
sin^2u =
= (1 - cos2u)/2
Power-Reducing Formula
cos^2u =
= (1 + cos2u)/2
Power-Reducing Formula
tan^2u =
= (1 - cos2u)/(1 + cos2u)
If a nonvertical line has inclination @ and slope m, then…
m = tan@
Finding an angle between two lines with slopes m1 and m2
tan@ = |(m1 - m2)/(1 + m1m2)|
Distance between the point (x,y) and the line Ax + By + C = 0
d = |Ax1 + By1 + C|/(√A^2 + B^2)
